As you’re talking about a 2 metre / 70cm dual band HT in the FT2DE, for SOTA work on a summit a favorite is the RH770 antenna that fastens to the antenna socket on the HT and has quite a long telescopic antenna on it (make sure you order one with the correct connector). This gives a major improvement over the standard “rubber duck” antenna. Of course you can then go up to J-poles (as Marton suggests) - you’d need one for 2m and one for 70cm or even a small beam - The Arrow and Elk range dual band beams come to mind but you’ll need a mast of some kind as well to support these options. For most situations in the UK, the RH-770 is probably adequate.
For mobile use on the Transit van, there are lots of options but the simplest would be a combined 1/4 wave 2m / 5/8 wave whip on a mag mount. Yes you can drill a hole and put a mount through the roof, however by going the mag mount route, you can take this antenna inside and slap it on top of a fridge or filing cabinet to use inside the house. Of course operation with an antenna inside the house isn’t going to be as good as having one outside, but for temporary use, for local contacts or accessing the local repeater it should work.
Mag mounts tend to come with an SO-239 socket hence you would need an antenna with a PL-259 plug on it. You could in theory use an adapter and put that RH-770 on the mag mount but it’s not really constructed for use in the winds on top of a moving vehicle, but for short term use or parked-up usage, it could be one antenna for all three needs (and it’s not expensive).
Whether you are running analogue FM or Digital - Yaesu Fusion, the antenna is the same. It’s vertically polarised.